Clear glass can have a wide range of chemistries. The glass used in windows on Earth is soda-lime glass, and is composed mostly of silicon dioxide, with some sodium oxide, and a small amount of a few other things. Pure silica sand, composed almost entirely of silicon dioxide, is common on Earth. The Moon has nothing like that. The proportion of silica in the minerals of the regolith is never more than half.
Most of the metal oxides in the regolith will form clear glass, if melted and then properly cooled to form a solid without a crystal structure, which is technically what glass is. The oxides of aluminum, magnesiium, calcium, and sodium will all do this just like silica does. Those metal oxides form 80 to 90 percent of the volume of most lunar minerals. Working with glass that is high in metal oxides other than silica can be more difficult - it could require higher heating and the glass may only be workable over a narrower temperature range.
A solar glass furnace would have little problem attaining the higher temperatures needed. The furnace and all glass forming equipment need to be made of materials that can withstand about 1200°C - no higher than all the equipment used to produce the refined feedstock for making the glass, and much less than the metal refining techniques discussed above.
The vacuum makes it easier to work with glass that has a narrow working temperature range. Heat is lost slowly and that can be slowed much more, simply by surrounding the working area in foil that reflects heat back into the system. Rather than having to reheat glass to anneal it (to relieve internal stresses that weaken the glass), the glass must be cooled, enough to have the desired viscosity to be put through rollers that extrude it as flat sheets. Sheet glass that is flat, or even better that has a curve to it, is what is really needed in giant quantities for many of the structures in the colonies. Radiators that gently chill the rollers can be used to put the glass at the right temperature to be properly formed, after which just putting a reflective tarp over the hot glass will slow cooling enough for it to anneal properly.
However, the 10 to 20 percent of the regolith mineral mix that isn't oxides of silicon, aluminum, calcium, magnesium, and sodium, must be removed almost completely or the glass will be strongly tinted or opaque. Iron turns it blue-green, titanium and sulfur yellow-brown, manganese purple, chromium dark green, and all of these are common enough in the regolith to have a strong effect. And there are a long list of others, some of which will discolor strongly at very low concentrations. Cobalt will yield blue glass at concentrations of 250 ppm.
Finding a deposit of highlands regolith that is very low in the undesired metals is the first thing to do. This shouldn't be too hard, and results could be much better if material can be obtained from rock instead of fine-grained regolith. Some highlands regolith is almost entirely plagioclase, so possibly the bedrock it came from is pure plagioclase. Plagioclase has none of the metals that are problematic, it's composed purely of oxides of light metals - aluminum, calcium, sodium, and silicon. If particles containing iron can be removed with magnets from powder plagioclase regolith, the remainder might be pure enough to make decently clear glass. The titanium is all in ilmenite, which also contains iron so would be removed by the magnetic separation. That might be enough.
Something of a tint to windows is vastly preferable to not having windows, and the lunar landscape is so colorless a tint to it could be regarded as an improvement. If glass could be produced in industrial quantities with the above process, which is fairly low-energy and low-tech, it would be an attractive option early on even if the resulting glass had a pretty clear tinge to it. But there is also another option.
The process of purifying olivine and pyroxene mentioned above in the solar furnace section could be applied to making clear glass. All of the minerals most common in the regolith that cause tinting fit into the crystal structure of pyroxene. The liquid poured off after pyroxene crystals have been pressed to the bottom of a vessel in a centrifuge will be made almost completely of oxides of silicon, aluminum, calcium, and sodium. Remaining minor components of the liquid aren't problematic - oxides of phosphorus and potassium, which are used in making glass on Earth and don't affect transparency.
As long as the regolith was toasted for a good while to remove its volatiles before being melted, this process as well could provide decently clear glass. The toasting especially needs to remove the sulfur, which otherwise will color glass yellow. This process is also technically simple. It requires more energy to perform, but mostly as heat which can be obtained from the sun, essentially for free once the equipment exists.
If purification by centrifuge worked well enough, any regolith feedstock could be used for this process. If it didn't work well enough the first time, repeating it could result in the purity required. Or, once again, selecting regolith from the highlands with a low content of troublesome minerals to begin with could yield a product good for clear glass after the first time through the centrifuge. Or, a centrifuge that presses the molten regolith with greater force could increase purity sufficiently. After all, centrifuges are another thing the Moon is very kind to - no atmospheric drag on the spinning vessels, and making frictionless magnetic bearings is a lot easier in the low gravity. Centrifuges benefit from this the same way flywheels do.
Freedom to include large quantities of clear glass in lunar architecture is tremendously beneficial. Where glazing uses the radiation blind design, or windows are sunk at the bottom of shafts that eliminate direct sight-lines to the sky, glass can be just a few centimeters thick - say, 8 cm (3"). That is still pretty thick, because it needs to support the pressure of the atmosphere, and that is a lot of force. The glass would need to be made of several laminated panes, to improve strength and prevent failure by shattering. If it can be thicker, then panes can be larger. Glazing means natural sunlight and a view of the sky. If you think it wouldn't bother you to live without either of those things, try it for a few days. A colony must have this, and have it over a sizable area so that everyone can enjoy it as much as they want.
Both of these processes can be scaled up as much as needed. With the infrastructure assembled to build a large number of giant glass furnaces, plate glass rolling equipment, and associated paraphernalia, Cernan's Promise is able to undertake construction of Lalande City. Such a city would not be possible otherwise.